MATH 230:  Introduction to Numerical Methods

 

Instructor:  Dr. Jianping Gan       Rm: 4621 (L1) and 4620 (L2);    Email: magan@ust.hk;       Tel: 7421;

                                                    Office hour:  Tue: 16:30-17:30

  

 

Teaching Assistant:  Qiaolin He (L1) and Lei Wang (L2)

 

Class schedule:

 

L1:                    11:00-11:50   Mon. and Wed.                                   Venue: 4621

L2:                    15:00-15:50   Mon. and Wed.                                   Venue: 4620

 

 

Textbook:

 

Numerical Analysis, 8th ed., by Burden, R.L. and Faires J. D., Thomson Brooks/Cole.

 http://www.as.ysu.edu/~faires/Numerical-Analysis

 

Course Web:

                     http://www.math.ust.hk/~magan/MATH230

Evaluation:

 

Home work:     10%

Mid-term   :      25%

Final          :      65%

 

Topics: (tentative topics are indicated by *)

 

Introduction to Computational World (Chapter 1)

 

 

Root Finding (Chapter 2)

  • Bisection method (2.1)
  • Fixed-point iteration (2.2)
  • Newton's method, Secant method (2.3)

Interpolation (Chapter 3)

  • Interpolation and the Lagrange (interpolating) polynomial (3.1)
  • Divided differences and Newton's interpolatory divided-difference formula (3.2)

Numerical Differentiation and Integration (Chapter 4)

  • Numerical differentiation--forward, backward, and central finite differences (4.1)
  • Elements of numerical integration (4.3)
  • Composite rules (4.4)
  • Gaussian quadrature--Gaussian node points, weights (4.7)

Solution of Ordinary Differential Equations (Chapter 5)

  • Euler's method (5.2)

 Solving Linear Systems (Chapters 6 & 7)

  • Gauss elimination--multipliers, Gauss elimination, back substitution, pivoting (6.1 - 6.2)
  • LU factorization--LU, forward substitution (6.5)
  • Iterative methods--matrix splitting, Jacobi method, Gauss-Seidel method, SOR method (7.3)

Approximation (Chapter 8)

  • Least squares data fitting--data fitting, modes, normal equation (8.1)
  • Fast Fourier Transforms* (8.6)

Eigenvalue Problem *(Chapter 9)

  • Power method (9.2)
  • QR algorithm (9.4)